Yes, Mr. Santorum has had a better run than anyone would have predicted even a few months ago. He appeals to conservative Republicans, Evangelicals, and those who really, really want an alternative to Romney.

But the math is not in his favor. In order to get the nomination, Santorum would need to win 69 percent of the remaining delegates – something which simply isn't going to happen.

His other hope – which he and his team have become more vocal about in recent days – is doing well enough to deny Romney the 1,144 delegates he needs, thereby delaying the decision until the August convention.

But that possibility is also incredibly slim, and would require a major screw-up by Romney. Currently, Romney only needs to win 46 percent of the remaining delegates to get to the magic number – not a high hurdle. The implosion of Newt Gingrich's campaign (he got just 8 percent of the vote in Illinois) hasn't helped Santorum the way some predicted, and might make it even harder to keep Romney from steadily amassing delegates.

Moreover, it's not something most Republicans want.

"Whatever slim chances that Mr. Santorum has would depend on going to the floor in Tampa," wrote New York Times polling expert Nate Silveron Wednesday, calling the nomination contest now "a one-man race." "As this becomes increasingly clear to voters, they may come to see their choice as being less one between Mr. Romney and Mr. Santorum and more one between Mr. Romney and a brokered convention. Some of Mr. Santorum’s supporters may desert him once they view the race in those terms, making Mr. Romney’s path easier still."

Add to that Santorum's fundraising deficits: In the past month, his campaign reported raising $9 million to Romney's $12 million, and the Santorum campaign has $2.6 million in the bank compared with Romney's $7.3 million.

Speaking to reporters after his thumping in Illinois Tuesday, Santorum refused to even acknowledge that he lost badly.

"It wasn't a tough night. We did very well," he said. "We picked up a lot of delegates tonight in a very tough state. Nobody had any expectations for us to win, and you know we did what we had to do."

He also put more pressure on Gingrich supporters to move over to him, saying, "it's very clear it’s a two-person race and now we need to get all the conservatives to line up behind us."

But if all of Gingrich's supporters had gone with Santorum in Illinois, the former Pennsylvania senator still would have lost.

Looking ahead, Santorum also doesn't get much help from the calendar.

Louisiana votes Saturday, and Santorum is expected to win there. But after that come a slew of Northern states where Romney is far better positioned. Of the states voting in April, Santorum has hope in Wisconsin, and in his home state of Pennsylvania, but that's about it.

So why stay in the race? Partly, it may have to do with denial – especially after such an unexpected Cinderella surge late in the campaign season. Or a wish to at least end on a good note, with a victory in Pennsylvania.

Santorum may also be hoping to garner more influence within the party, especially its growing conservative wing.

But expect increased calls, both publicly and behind the scenes, for Santorum to acknowledge what almost everyone else seems to have realized.

Mr. Fehrnstrom replied that he understands the "emotion and the hard work and the sweat that goes into a campaign" and what a personal decision it is to step down – but then made it clear he believes Romney's opponents are in denial.

"At some point the reality is going to set in that Mitt is the all-but-certain nominee," Fehrnstrom said. "I can tell you what Mitt Romney did four years ago when he found himself in the similar situation running against John McCain. After Super Tuesday, John McCain certainly didn’t have the delegates to become the nominee, but he was on track to get those delegates and Mitt Romney made the decision – and it was a difficult one – to step aside. And he stepped aside because he thought it was good for the country."